The position of a particle moving along a straight line, in meters, is given by s= 6/t, where t represents time, in seconds. Calculate the average velocity of the particle, in meters per second, on the time interval [1,3]

The average velocity of the particle on the time interval is -2 meters per second.

Step-by-step explanation:

Let be the position curve which is continuous on the time interval . The average velocity (), measured in meters per second, on the time interval is represented by the following expression:

Where:

, - Initial and final times, measured in seconds.

, - Initial and final positions, measured in meters.

If we know that , and , the average velocity of the particle on the time interval is:

The average velocity of the particle on the time interval is -2 meters per second.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for